Related papers: Convex Hybrid Modeling: An Operator-Based Approach
Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art…
Small additive ensembles of symbolic rules offer interpretable prediction models. Traditionally, these ensembles use rule conditions based on conjunctions of simple threshold propositions $x \geq t$ on a single input variable $x$ and…
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
To address the issues of stability and fidelity in interpretable learning, a novel interpretable methodology, ensemble interpretation, is presented in this paper which integrates multi-perspective explanation of various interpretation…
Still under debate is the question of whether machine learning is capable of going beyond black-box modeling for complex physical systems. We investigate the generalizing and interpretability properties of learning algorithms. To this end,…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
Several researchers have argued that a machine learning system's interpretability should be defined in relation to a specific agent or task: we should not ask if the system is interpretable, but to whom is it interpretable. We describe a…
Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that…
With dramatic breakthroughs in recent years, machine learning is showing great potential to upgrade the toolbox for power system optimization. Understanding the strength and limitation of machine learning approaches is crucial to decide…
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…
Machine Learning (ML) models are often complex and difficult to interpret due to their 'black-box' characteristics. Interpretability of a ML model is usually defined as the degree to which a human can understand the cause of decisions…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
There are two things to be considered when we evaluate predictive models. One is prediction accuracy,and the other is interpretability. Over the recent decades, many prediction models of high performance, such as ensemble-based models and…
The development of the works of the author about adaptive algorithms of teaching the robotic systems with the help of operator is described here. An operator is assumed to be an experience decision-maker and sane carrier of a target which…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
Deep neural networks have been well-known for their superb handling of various machine learning and artificial intelligence tasks. However, due to their over-parameterized black-box nature, it is often difficult to understand the prediction…